Documentation

Linglib.Studies.RotterLiu2025

[RL25]: A Register Approach to Modal (Non-)Concord in English #

Modal concord (MC) doubles a modal verb and a modal adverb of the same force (may possibly, must certainly) versus the single modal (SM, may / must). [RL25] asks whether MC differs from SM in meaning and social perception, and whether that difference is register-sensitive (varies with situational context). Its Experiment 1 is the no-context study [LR25] (formalized in Studies/LiuRotter2025); Experiment 2, formalized here, adds a CONTEXT factor — interlocutor relation, close vs distant — in a 2×2×2 (NUMBER × FORCE × CONTEXT) design (306 participants, Prolific).

Two analyses make precise, divergent predictions ([RL25] (3a)/(3b)):

They differ only for universal modals. Experiment 2 replicates Experiment 1: the necessity strengthening (which adjudicates for spread), the possibility weakening (a residual neither analysis predicts, [RL25] §4.1), the confidence crossover, the warmth penalty, and lower grammaticality/appropriateness for MC. Crucially (RQ4) no NUMBER × CONTEXT interaction appears for any measure: MC's effect is not register-sensitive to interlocutor relation.

Main definitions #

Main results #

Implementation notes #

Reuses the sign-prediction machinery of Studies/LiuRotter2025 (ShiftObservation, cellMean, forceKey, the rival accounts). Cell means live in Data.Examples.RotterLiu2025 (×100, on the 1–7 scale); they do not reduce in the kernel, so concrete shifts are computed via #eval while the kernel-checkable content is each analysis's systematic prediction.

The two analyses (precise predictions) #

@[reducible, inline]

The concord analysis ([Zei07]): MC is truth-conditionally equivalent to SM, so doubling has no commitment effect — the force-blind null LiuRotter2025.vacuityEffect.

Equations
Instances For

    The modal-spread analysis ([GM18]) as [RL25] state it ((3a)/(3b)): doubling strengthens commitment for universal modals (must certainly > must) but only maintains the default for existential modals (may possibly = may).

    Equations
    Instances For

      The two analyses agree for existential modals (no change) and differ only for universal modals — the single locus where the data can adjudicate ([RL25] (3a) vs (3b)).

      Predicting against the data #

      Each cell of Data.Examples.RotterLiu2025 carries the Experiment 2 means (×100) for one CONTEXT × FORCE × NUMBER combination. An analysis predicts the sign of the concord shift MC − SM per force; the observed sign is read off the paired cell means.

      def RotterLiu2025.findCell (context force number : String) :

      The cell with the given context / force / number paperFeatures.

      Equations
      • One or more equations did not get rendered due to their size.
      Instances For

        The observed MC − SM shift for measure in context under force.

        Equations
        • One or more equations did not get rendered due to their size.
        Instances For

          The universal case adjudicates: must certainly > must carries the strengthening sign the spread analysis predicts and the concord analysis does not.

          The existential weakening is a residual: may possibly < may carries a sign that neither analysis predicts — both predict maintenance ([RL25] §4.1).

          Register (in)sensitivity — RQ4 #

          The headline null result: no NUMBER × CONTEXT interaction. Structurally, a CONTEXT main effect shifts the MC and SM means by the same amount, so it cancels in the concord contrast MC − SM and cannot change its sign.

          A concord effect is register-sensitive (for this CONTEXT parameter) when its shift differs in sign between the close and distant contexts — a NUMBER × CONTEXT interaction at the level of sign.

          Equations
          Instances For
            theorem RotterLiu2025.context_main_effect_preserves_sign (o : LiuRotter2025.ShiftObservation) (c : ) :
            { force := o.force, mcMean := o.mcMean + c, smMean := o.smMean + c }.observedSign = o.observedSign

            A CONTEXT main effect (the same additive shift c on MC and SM) leaves the concord shift's sign unchanged: it cancels in MC − SM.

            theorem RotterLiu2025.not_registerSensitive_of_main_effect (o : LiuRotter2025.ShiftObservation) (c : ) :
            ¬RegisterSensitive o { force := o.force, mcMean := o.mcMean + c, smMean := o.smMean + c }

            RQ4 ([RL25]): when contexts differ only by a main effect, the concord shift is not register-sensitive — close and distant carry the same sign, so no NUMBER × CONTEXT interaction arises.

            Relationship to Experiment 1 ([LR25]) #

            The replication is exact at the level of accounts on the necessity side, and the one mismatch on the possibility side is precisely the residual: [LR25]'s spreadEffect records the observed weakening (−1), whereas the spread analysis predicts maintenance (0).

            On necessity, Experiment 2's strengthening matches the spread prediction and the crossover sign [LR25] reports for Experiment 1.

            On possibility, [LR25]'s observed spreadEffect (−1) diverges from the spread analysis's prediction (0): the gap is the residual that possibility_residual isolates.

            The observed shifts #

            The #evals exhibit Experiment 2's findings (means do not reduce in the kernel, so these are computed). The commitment and confidence crossovers and the warmth and appropriateness penalties hold in both contexts, and the commitment sign is context-invariant per force — the RQ4 null in the data.